Has an MLB game ever ended 15-13?
It has. 15-13 has been a MLB final 20 times in 235,971 games. The first was Cincinnati Reds beat Philadelphia Athletics on September 13, 1876; the latest was Atlanta Braves beat Philadelphia Phillies on May 2, 2012.
That makes 15-13 the 173rd most common final score out of 330 that have ever occurred in MLB. One point away, 16-13 has happened 19 times and 15-14 has happened 27 times. At one point the score disappeared for 33 years, between 1901 and 1934.